Algebra Examples

$x^{4} - x^{3} - 6 x^{2}$

Step 1

Factor $x^{2}$ out of $x^{4} - x^{3} - 6 x^{2}$ .

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Step 1.1

Factor $x^{2}$ out of $x^{4}$ .

$x^{2} x^{2} - x^{3} - 6 x^{2}$

Step 1.2

Factor $x^{2}$ out of $- x^{3}$ .

$x^{2} x^{2} + x^{2} (- x) - 6 x^{2}$

Step 1.3

Factor $x^{2}$ out of $- 6 x^{2}$ .

$x^{2} x^{2} + x^{2} (- x) + x^{2} \cdot - 6$

Step 1.4

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} (- x)$ .

$x^{2} (x^{2} - x) + x^{2} \cdot - 6$

Step 1.5

Factor $x^{2}$ out of $x^{2} (x^{2} - x) + x^{2} \cdot - 6$ .

$x^{2} (x^{2} - x - 6)$

Step 2

Factor.

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Step 2.1

Factor $x^{2} - x - 6$ using the AC method.

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Step 2.1.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Step 2.1.2

Write the factored form using these integers.

$x^{2} ((x - 3) (x + 2))$

Step 2.2

Remove unnecessary parentheses.

$x^{2} (x - 3) (x + 2)$